共查询到20条相似文献，搜索用时 31 毫秒
1.
In solving groundwater transport problems with numerical models, the computation time (CPU processing time) of transport simulation is approximately inversely proportional to the transport time-step size. Therefore, large time-step sizes are favorable for achieving short computation time. However, transport time-step size must be sufficiently small to avoid numerical instability if an explicit scheme is used (and to guarantee enough model accuracy if an implicit scheme is used). For a transport model involving groundwater pumping, a small transport time-step size is often required due to the high groundwater velocities near the pumping well. Small grid spacing often specified near the pumping well also limits the time-step size. This paper presents a method to increase transport time-step size in a transport model when groundwater pumping is simulated. The key to this approach is to numerically decrease the groundwater seepage velocities in grid cells near the pumping well by increasing the effective porosity so that the transport time-step size can be increased without violating stability constraints. Numerical tests reveal that by using the proposed method, the computation time of transport simulation can be reduced significantly, while the transport simulation results change very little. 相似文献
2.
Jan O. Backhaus 《Continental Shelf Research》1982,2(4):243-254
A semi-implicit scheme for the numerical solution of the shallow water equations is proposed. The scheme is suitable for the simulation of shelf sea dynamics as is demonstrated by some examples of successful application covering a range of grid sizes typical for shelf sea models. The basic outlines of the method are presented. Some practical aspects of computation are discussed which illustrate that an explicit model can be modified easily to the semi-implicit version proposed here. Compared to explicit schemes the semi-implicit approach has two major advantages: (1) its economy (a saving of at least 50% in computing time can be achieved); (2) a closer match is obtained between the time-stepping procedure and the time scales of processes, the spatial scales of which are close to the lower limit of the resolution of the model grid. 相似文献
3.
在数值模拟中,隐式有限差分具有较高的精度和稳定性.然而,传统隐式有限差分算法大多由于需要求解大型矩阵方程而存在计算效率偏低的局限性.本文针对一阶速度-应力弹性波方程,构建了一种优化隐式交错网格有限差分格式,然后将改进格式由时间-空间域转换为时间-波数域,利用二范数原理建立目标函数,再利用模拟退火法求取优化系数.通过对均匀模型以及复杂介质模型进行一阶速度-应力弹性波方程数值模拟所得单炮记录、波场快照分析表明:这种优化隐式交错网格差分算法与传统的几种显式和隐式交错网格有限差分算法相比不但降低了计算量,而且能有效的压制网格频散,使弹性波数值模拟的精度得到有效的提高. 相似文献
4.
Explicit integration procedures have been widely adapted and applied to hybrid simulations of the seismic response of structures due to their simplicity. However, these procedures are only conditionally stable and have limited recent applications of hybrid simulations to simple structural models with few degrees of freedom. A novel integration procedure is proposed herein, in which a fully implicit formulation is applied to solve the equation of motion for the hybrid model, but defaults to an explicit or noniterative formulation in steps that fail to converge. The advantages to this approach are the ensured continuity of the simulation and the reduced accumulation of errors that occur during consecutive explicit steps that may lead to instability. The implicit procedure is applied by loading the experimental substructures beyond the expected displacement for the current step, then using the displacements and forces measured through the load path in the iterative implicit scheme. This approach captures the instantaneous behaviour of experimental substructures without physically imposing iterations. Numerical and experimental simulations demonstrate the effectiveness of the proposed integration scheme for multi‐degree‐of‐freedom models, especially in utilization of longer time steps that exceed stability limits of explicit methods, prevention of excitation of higher modes, and testing of stiff systems. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
We present a fully implicit numerical method to solve the incompressible MHD equations in a strongly rotating Cartesian domain. The equations are solved in a primitive variable formulation using a finite volume discretization. In order to use massively parallel computers, we applied a domain decomposition approach in space. The performance of this model is compared with an earlier model, which treated the convective terms of the equations in an explicit manner. Our results indicate that although the fully implicit method needs about three times the memory of the implicit–explicit method, it is superior in terms of computational efficiency. As an application of this model, we investigated the influence of the Prandtl number in the range of 0.01–1000 on the dynamics of the dynamo. 相似文献
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7.
The dynamic analysis of complex non-linear structural systems by the finite element approach requires the use of time-step algorithms for solving the equations of motion in the time domain. Both an implicit and an explicit version of such a time-step algorithm, called the ρ-method, the parameter ρ being used for controlling numerical damping in the higher modes, are presented in this paper. For the implicit family of algorithms unconditional stability, consistency, convergence, accuracy and overshoot properties are first discussed and proved. On the basis of the algorithmic damping ratio (dissipation) and period elongation (dispersion) the ρ-method is then compared with the well-known implicit algorithms of Hilber, Newmark, Wilson, Park and Houbolt. An explicit version of the algorithm is also derived and briefly discussed. This shows numerical properties similar to the central difference method. Both versions of the algorithm have been implemented in a general purpose computer program which has been often used for both numerical tests and practical applications. 相似文献
8.
Cheng-Chin Wu 《地球物理与天体物理流体动力学》2013,107(1):37-61
We present a high order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of incompressible fluid dynamics and magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme that has been successfully applied to compressible fluids, with or without magnetic fields. A fractional time-step method is used to enforce the incompressibility condition. Two basic elements of the WENO scheme, upwinding and wave decomposition, are shown to be important in solving the incompressible systems. Numerical results demonstrate that the scheme performs well for one-dimensional Riemann problems, a two-dimensional double-shear flow problem, and the two-dimensional Orszag–Tang MHD vortex system. They establish that the WENO code is numerical stable even when there are no explicit dissipation terms. It can handle discontinuous data and attain converged results with a high order of accuracy. 相似文献
9.
We recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement‐stress formulations on staggered grids using explicit finite‐difference, pseudo‐implicit finite‐difference and pseudo‐spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated staggered‐grid modelling for isotropic medium, 2D staggered‐grid modelling for vertically transversely isotropic medium and 2D rotated staggered‐grid modelling for tilted transversely isotropic medium. 相似文献
10.
Introduction In linear elastic medium,motion equation for lumped-mass finite element simulation of wave motion is expressed as(LIAO,2002)∑=+lililii ttGtM)()()(FUU&&(1)where Mi is lumped-mass at node i,Gil is stiffness coefficient of node i with respect to node l,üi(t)is acceleration vectors at node i,Ul(t)is displacement vectors at node l,Fi(t)is the external nodal force vectors acting at node i.If acceleration vectorsüi(t),displacement vectors Ul(t)and the external nodal force vectors… 相似文献
11.
时域有限差分(FDTD)方法使用Yee网格剖分电磁场的空间采样,通过时间步迭代实现电磁场数值模拟,具有内存消耗低、计算简单等特点,常用于瞬变电磁三维正演.然而,常规FDTD方法的时间迭代步长Δt受Courant-Friedrich-Lewy(CFL)条件严格限制,过多的迭代次数以及过密的采样往往导致计算速度慢、累积误差不断增大.本文提出一种不受CFL条件约束的无条件稳定隐式差分算法Crank-Nicolson FDTD(CN-FDTD)用于瞬变电磁三维正演.基于Crank-Nicolson差分方法对Maxwell方程组重新离散,空间网格仍然采用Yee元胞,时间步进采用在整时间步电场、磁场同时采样的策略,建立无条件稳定FDTD格式,突破CFL条件限制.与常规FDTD交替采样相比,CN-FDTD电场、磁场同时采样的策略构成的隐式差分格式,需要求解大型稀疏矩阵方程组.通常,瞬变电磁三维正演模型中产生的矩阵阶数往往较大,需要占用大量内存和求解时间.为解决上述问题,采用Crank-Nicolson-cycle-sweep-uniform(CNCSU-FDTD)方法近似求解CN-FDTD方程,在保证求解精度的同时,计算效率大幅提高.在边界条件处理上,采用双线性变换推导了复频率参数完全匹配层(CFS-PML)吸收边界.采用均匀半空间模型、四类三层模型进行精度验证,发现CN-FDTD三维正演结果与解析解、线性数字滤波解吻合较好.之后,与接触带上的低阻复杂模型进行对比,结果显示CN-FDTD正演结果与矢量有限元、有限体积法以及FDTD计算结果吻合较好.在此基础上,研究了时间步放大对CN-FDTD计算精度的影响,发现最大时间步放大到常规FDTD的3200倍时才会在晚期出现较明显的误差.在一台CPU为Intel Core i5-7300HQ的笔记本电脑单线程计算条件下,模拟到关断后30 ms仅需要50 min.在进行并行化后,将有望实现复杂模型分钟级的三维正演,从而为三维反演提供可靠、快速的正演方法. 相似文献
12.
The first-order accurate explicit finite-difference scheme based on the method of characteristics (MOC) has been widely used for the analysis of waterhammer in pipelines. For the stability of this scheme, the Courant condition has been developed by neglecting the nonlinear terms. When the friction loss term is large, this scheme becomes unstable even if the Courant stability is satisfied. In this paper, the stability and accuracy including friction are investigated by systematically analyzing typical piping systems over a wide range of parameters and empirical stability limits are presented for practical applications. In addition, the suitability of the implicit finite difference method for transient analysis is investigated. 相似文献
13.
A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena. 相似文献
14.
We present a comparison of methods for the analysis of the numerical substructure in a real‐time hybrid test. A multi‐tasking strategy is described, which satisfies the various control and numerical requirements. Within this strategy a variety of explicit and implicit time‐integration algorithms have been evaluated. Fully implicit schemes can be used in fast hybrid testing via a digital sub‐step feedback technique, but it is shown that this approach requires a large amount of computation at each sub‐step, making real‐time execution difficult for all but the simplest models. In cases where the numerical substructure poses no harsh stability condition, it is shown that the Newmark explicit method offers advantages of speed and accuracy. Where the stability limit of an explicit method cannot be met, one of the several alternatives may be used, such as Chang's modified Newmark scheme or the α‐operator splitting method. Appropriate methods of actuator delay compensation are also discussed. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
15.
Newm ark-更新精细积分法是动力方程求解的隐式的时域逐步积分法,其稳定性条件非常容易满足。与隐式方法相比较,显式积分方法不需要求解耦联的方程组,可以有效地减少内存占用和机时耗费。因此,根据显式积分方法的特点和优点,基于Newm ark-更新精细积分法的基本思想,提出其显式积分格式。对显式积分方法的精度与稳定性进行了初步的分析,指出该显式积分方法具有极好的稳定性,其精度比隐式积分方法的精度稍低。随着时间步长的增加,其精度优于传统的方法。 相似文献
16.
湖泊三维风生流隐式差分模型的研究 总被引：1，自引：0，他引：1
建立了湖泊三维风生流的隐格式差分模型,通过对该模型计算稳定性的分析发现,它的时间步长的取值具有较大的灵活性．该模型波用于武汉市墨水湖的民生流模拟,实例计算表明该模型计算结果合理,能较好地反映湖泊风生流的流态特征． 相似文献
17.
有限差分方法广泛应用于求解许多科技领域所涉及的偏微分方程,高阶显式有限差分方法通常用来提高求解精度,已经提出的高阶隐式有限差分方法和截断高阶显式有限差分方法可用来进一步提高模拟精度而不增加计算量。本文首先计算了针对常规网格上的一阶导数和二阶导数、交错网格上的一阶导数的有限差分系数,发现高阶隐式有限差分系数中存在一些小的系数。频散分析结果表明:忽略这些小的差分系数能够近似维持有限差分的精度,但是显著减小了计算量。然后,引入镜像对称边界条件来提高隐式有限差分方法的精度和稳定性,采用混合吸收边界条件来减小来自模型边界所不需要的反射。最后,给出了针对均匀和非均匀介质模型的弹性波模拟例子,表明了本文方法的优点。 相似文献
18.
应用二阶算子分裂格式,采用全非线性模式,对可压大气中重力波波包非共振激发进行数值模拟和分析.研究表明：两个向上传播的重力波波包,通过非共振相互作用,也能激发出一个向下传播的重力波波包.生成波的能量几乎正比于主波的能量,也随次波的能量增大而增大.能量传递方向主要表现为从高频的主波向次波和生成波转移,这与共振相互作用不完全相同.非共振作用的特征时间由主次波的初始位置和波长频率决定,与主次波的初始振幅无关.生成波的波矢量并不严格满足弱非线性相互作用理论预言的波矢量匹配条件,而且生成波的波长和频率在传播的过程中会随时间发生变化,这表明了弱非线性相互作用理论的局限性. 相似文献
19.
地震波传播过程本质上是能量在传播过程中逐步损耗直至殆尽的过程，而在实际应用中，常在无能量损耗假设下，用弹性波动方程或标量波动方程描述它.在哈密顿(Hamilton)体系表述下，地震波传播过程即为一个无限维的哈密顿系统随时间的演化过程.若不计能量损耗，波场演化过程实质上为一个单参数连续的辛变换，因而对应的数值算法应为辛几何算法.本文首先从地震波标量方程出发，给出哈密顿体系下地震波传播的表述，即任意两个时刻的波场是通过辛变换联系起来的.随后，把波场在时间和相空间离散化后，给出了用于波场计算的一些辛格式，如显式辛格式、隐式辛格式和蛙跳辛格式.并进一步讨论了有限差分格式和辛格式的异同.然后，应用显式辛格式和同阶的有限差分方法给出了同一理论速度模型下的波场和Marmousi速度模型下的单炮记录.数值结果表明，辛算法是一类可行的波场模拟的数值算法.在时间步长较小时，有限差分方法是辛算法的一个很好近似.文中的理论和方法，为地震波传播理论及实际应用研究提供了新的途径. 相似文献
20.
A distributed overland flow model is presented and the test results compared with those of the unit hydrograph (UH) model. Infiltration excess in the overland model was calculated using both a modified Green and Ampt (G–A) method and a more complicated method that keeps track of the soil moisture content. The two‐dimensional partial differential flow equations with kinematic flow approximation were solved using both backward‐central explicit and implicit finite‐difference schemes. Moreover, a baseflow component was added to the flow model. Each part of the model was built by replacing a process by a parallel process or by adding a completely new component. When the model was developed and validated in small agricultural fields in southern Finland, comparisons were made between corresponding processes and the significance of added components were estimated in order to find out whether increased model complexity improves the model performance. Apart from the basic model, all the other distributed models outperformed the UH approach. The implicit scheme was clearly more accurate than the explicit scheme, and the baseflow component improved the results significantly. There was no major difference between the performances of the infiltration models, but the G–A method was more stable and much faster. The approaches that were best in the calibration were also the best in the verification. The full distributed model provides a potential method for running water‐quality models and testing their different processes. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献